We consider a diatomic molecule in a two-mode optical cavity (cf. Fig.REF (a)) described by an effective length-gauge, rovibrational Pauli-Fierz Hamiltonian in dipole and cavity Born-Oppenheimer type approximation[1]}, [2]}, [3]}, [4]}, as given by
\(\hat{H}=\hat{H}_S+\hat{H}_C+\hat{H}_{SC}+\hat{H}_{DSE}\quad .\) 
